Question

Tg(p/4+a)×tg(p/4-a)​

Answer 1

ОТВЕТ:. *1*

~•~•~•ZLOY_TIGROVSKIY~•~•~•

Answer 2

The expression you've provided, "tg(p/4+a)×tg(p/4-a)", appears to be the product of two tangent functions with different arguments. In trigonometry, the tangent of the sum of two angles is not directly simplified into a simple expression like the sine or cosine of a sum of angles. However, you can expand this expression using trigonometric identities.

Let's start by using the tangent sum formula, which states:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

In your expression, A = p/4 + a and B = p/4 - a. So, we can substitute these values into the formula:

tan(p/4 + a) * tan(p/4 - a) = [tan(p/4 + a) + tan(p/4 - a)] / [1 - tan(p/4 + a) * tan(p/4 - a)]

Now, we need to find the tangent values for p/4 + a and p/4 - a. To do this, we can use the tangent of a sum formula again:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

For A = p/4 and B = a: tan(p/4 + a) = (tan(p/4) + tan(a)) / (1 - tan(p/4) * tan(a))

For A = p/4 and B = -a: tan(p/4 - a) = (tan(p/4) - tan(a)) / (1 + tan(p/4) * tan(a))

Now, we can substitute these values back into the original expression:

[tan(p/4 + a) + tan(p/4 - a)] / [1 - tan(p/4 + a) * tan(p/4 - a)]

= [(tan(p/4) + tan(a)) / (1 - tan(p/4) * tan(a))] + [(tan(p/4) - tan(a)) / (1 + tan(p/4) * tan(a))]

= (tan(p/4) + tan(a)) / (1 - tan(p/4) * tan(a)) + (tan(p/4) - tan(a)) / (1 + tan(p/4) * tan(a))

This is the expanded form of the expression "tg(p/4+a)×tg(p/4-a)." Depending on the specific values of p and a, you may be able to simplify it further.